Question

plZ solve first revelent answer will be marked as brainliest​

Answer 1

Step-by-step explanation:

a=4

Step-by-step explanation:

refer to the attachment

Hope it helps!

(pls Mark it the Brainliest^^)

Answer 2

Required to find :-

• Value of " a " ?

Solution :-

Given information :-

$\tt a + \sqrt{15} = \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

We need to find the value of ' a '

So,

Consider the RHS part ;

$\dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

Here,

We need to rationalise the denominator

Rationalising factor of √5 - √3 = √5 + √3

So,

Multiply both numerator and denominator with the rationalising factor

$\dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

However,

We need to use some algebraic identities ;

They are ,

• 1. ( x + y ) ( x + y ) = ( x + y )²

• 2. ( x + y ) ( x - y ) = x² - y²

• 3. ( x + y )² = x² + y² - 2xy

So, using the 1st and 2nd we get

$\dfrac{( \sqrt{5} + \sqrt{3} {)}^{2} }{( \sqrt{5} {)}^{2} - ( \sqrt{3} {)}^{2} }$

Expand the numerator using the 3rd identity ;

$\dfrac{( \sqrt{5} {)}^{2} + ( \sqrt{3} {)}^{2} + 2( \sqrt{5})( \sqrt{3} ) }{5 - 3}$

$\dfrac{5 + 3 + 2 \sqrt{15} }{2}$

$\dfrac{8 + 2 \sqrt{15} }{2}$

$\dfrac{2(4 + \sqrt{15}) }{2}$

2 gets cancelled in both numerator and denominator

$4 + \sqrt{15}$

Now compare the LHS and RHS

$a + \sqrt{15} = 4 + \sqrt{15}$

From the above comparison we can conclude that ;

Hence,

Value of ' a ' = 4